Author | Hsiang, Wu Yi. author |
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Title | Cohomology Theory of Topological Transformation Groups [electronic resource] / by Wu Yi Hsiang |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1975 |
Connect to | http://dx.doi.org/10.1007/978-3-642-66052-8 |
Descript | X, 166 p. online resource |
I. Generalities on Compact Lie Groups and G-Spaces -- ยง 1. General Properties of Compact Topological Groups -- ยง 2. Generalities of Fibre Bundles and Free G-Spaces -- ยง 3. The Existence of Slice and its Consequences on General G-Space -- ยง4. General Theory of Compact Connected Lie Groups -- II. Structural and Classification Theory of Compact Lie Groups and Their Representations -- ยง 1. Orbit Structure of the Adjoint Action -- ยง 2. Classification of Compact Connected Lie Groups -- ยง 3. Classification of Irreducible Representations -- III. An Equivariant Cohomology Theory Related to Fibre Bundle Theory -- ยง 1. The Construction of HG*(X) and its Formal Properties -- ยง 2. Localization Theorem of Borel-Atiyah-Segal Type -- IV The Orbit Structure of a G-Space X and the Ideal Theoretical Invariants of HG*(X) -- ยง 1. Some Basic Fixed Point Theorems -- ยง 2. Torsions of Equivariant Cohomology and F-Varieties of G-Spaces -- ยง 3. A Splitting Theorem for Poincarรฉ Duality Spaces -- V. The Splitting Principle and the Geometric Weight System of Topological Transformation Groups on Acyclic Cohomology Manifolds or Cohomology Spheres -- ยง 1. The Splitting Principle and the Geometric Weight System for Actions on Acyclic Cohomology Manifolds -- ยง 2. Geometric Weight System and Orbit Structure -- ยง 3. Classification of Principal Orbit Types for Actions of Simple Compact Lie Groups on Acyclic Cohomology Manifolds -- ยง4. Classification of Connected Principal Orbit Types for Actions of (General) Compact Connected Lie Groups on Acyclic Cohomology Manifolds -- ยง 5. A Basis Fixed Point Theorem -- ยง 6. Low Dimensional Topological Representations of Compact Connected Lie Groups -- ยง 7. Concluding Remarks Related to Geometric Weight System -- VI. The Splitting Theorems and the Geometric Weight System of Topological Transformation Groups on Cohomology Projective Spaces -- ยง 1. Transformation Groups on Cohomology Complex Projective Spaces -- ยง 2. Transformation Groups on Cohomology Quaternionic Projective Spaces -- ยง 3. Structure Theorems for Actions of ?p-Tori on ?p-Cohomology Projective Spaces (p Odd Primes) -- ยง4. Structure Theorems for Actions of ?2-Tori on ?2-Cohomology Projective Spaces -- VII Transformation Groups on Compact Homogeneous Spaces -- ยง 1. Topological Transformation Groups on Spaces of the Rational Homotopy Type of Product of Odd Spheres -- ยง2. Degree of Symmetry of Compact Homogeneous Spaces -- References